Simple way to create a curved tunnel between two planes
Create a mesh circle, in Edit Mode rotate it $90º$ in the X axis.

Erase three quarters of it and move the remaining vertex along the X axis to the side.

Add a Screw modifier and adjust the axis and Steps parameters accordingly (multiples of 4 are advised). Apply the modifier or convert (a copy of) the object to mesh afterwards.



Add a new plane mesh, scale it as desired then erase all faces leaving only the edges. Subdivide them to match the previously chosen value for Steps in the screw modifier.

Follow the formula $\frac{Steps}{4}-1$ for the subdivision value. In my case I set $64$ Steps so $\frac {64}{4} - 1 = 15$ .

Join the plane to the circle at the correct height with Ctrl + J, then bridge the gaping edge loops with the Bridge Edge loops operator.

Now add a Mirror modifier along the $Z$ axis to complete the symmetry.



If you need an even mesh density you may optionally add a few edge loops to the bridged faces.